Based on the generalized coupled thermoelasticity in the Lord-Shulman (L-S) model, the state equation of infinite functionally graded plates were established by using of the Laplace transform and state space approach, in which the displacement, temperature and their first derivatives were chosen as state variables. As a numerical example, a functionally graded plate with the material properties changing by exponential law distribution along the thickness of plate, subjected to thermo-mechanical shock was considered. By employing the numerical inversion of the Laplace transform, numerical result showing the temperature, the displacement and stress components changing with the time are represented graphically. Characteristics of the propagation of the thermal elastic wave are also analyzed.